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Showing the Lift Equation in its
Y = mX + b Form
Answers
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the problems.
NAME__________________________________ CLASS__________
1a. Identify each letter in the lift equation and list the units
for each.
Cl
= Lift Coefficient (no
units)
L
= Lift
(newtons)
r
= Density of Air
(kg/m3)
V
= Velocity
(m/s)
A
= Area of Wing
(m2)
1b. Identify each letter in the lift equation and list the units
for each.
Cl
= Lift Coefficient (no
units)
a
= Angle of Attack (radiians no
units)
Clo
= Lift Coefficient at
a
= zero (no units)
2. Write out the two equations for the value of Cl.
Cl = L / (r *
V2 / 2 * A).
Cl = 2 *
p
* a
+ Clo
3. Rearrange the two equations and solve for L as a function of
a.
L = (2 * p
* a
+ Clo) * (r * V2 / 2 * A)
OR
L = (2 * p
* r * V2 / 2 * A) * a
+ (Clo * r * V2 / 2 * A)
Notice this is in the form
Y
=
mX
+
b.
L
=
(2 * p
* r * V2 / 2 * A)
*
a
+
(Clo * r * V2 / 2 *
A)
Y = dependent
variable,
X = independent
variable,
m =
slope,
b = Y
intercept.
4. Record the values shown:
L = 3,030
newtons
A = 2 square
meters
V = 160 km/hr = 44.4
m/sec
r =
1.23 kg/m cubed
a =
zero
Clo
= 2 * L / r * v squared * A =
1.24
5 & 6
Calculated numbers may vary slightly from those
shown below due to round-off errors.
angle in degrees
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angles in radians
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calculated values of lift
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value of lift from Foilsim
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-20
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-.3491
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-2291
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-3024
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-15
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-.2618
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-959
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-1523
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-10
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-.1745
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372
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-1.8
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-5
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-.08726
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1704
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1520
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0
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0
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3036
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3030
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5
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.08726
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4367
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4517
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10
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.1745
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5699
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5970
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15
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.2618
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7031
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7278
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20
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.3491
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8363
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8729
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The
plots are different.
This is due to the fact that the thin airfoil equation contains an
approximation that is only good at small values of
a . Foilsim does not use this
approximation.
7. The value of lift scales linearly as a
function of the area of the wing as can be seen by the linear change
in the value of lift.
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